A bouncy ball is dropped such that the height of its first bounce is 2.75 feet and each
successive bounce is 69% of the previous bounce's height. Write a recursive formula
to represent the height of the nth bounce of the ball.
The value 2.75 goes in the first box, since it's the first term.
The expression [tex]0.69*a_{n-1}[/tex] goes in the second box. The second line says "to get the nth term, we multiply the previous term by 0.69"
How can we simplify this expression below into a single logarithm? 3log(x)+1/2log(4y)−log(z)
Answer:
[tex]log(\frac{2x^3\sqrt{y} }{z} )[/tex]
Step-by-step explanation:
We can start by using the power property of logarithms to rewrite the expression. We raise the contents of the logarithm to the power of the coefficient:
[tex]log(x^3) + log([4y]^\frac{1}{2} )-log(z)\\log(x^3) + log(2\sqrt{y})-log(z)[/tex]
Now, we can use both the addition and subtraction properties of logarithms to rewrite the expression. Addition becomes multiplication while subtraction becomes division:
[tex]log(\frac{x^3*2\sqrt{y}}{z} )[/tex]
And to write it in a more proper way:
[tex]log(\frac{2x^3\sqrt{y} }{z} )[/tex]
What is the decay factor of the exponential function
represented by the table?
Given:
The table of values of an exponential function.
To find:
The decay factor of the exponential function.
Solution:
The general form of an exponential function is:
[tex]y=ab^x[/tex] ...(i)
Where, a is the initial value and [tex]0<b<1[/tex] is the decay factor and [tex]b>1[/tex] is the growth factor.
The exponential function passes through the point (0,6). Substituting [tex]x=0,y=6[/tex] in (i), we get
[tex]6=ab^0[/tex]
[tex]6=a(1)[/tex]
[tex]6=a[/tex]
The exponential function passes through the point (1,2). Substituting [tex]x=1,y=2,a=6[/tex] in (i), we get
[tex]2=6(b)^1[/tex]
[tex]2=6b[/tex]
[tex]\dfrac{2}{6}=b[/tex]
[tex]\dfrac{1}{3}=b[/tex]
Here, [tex]b=\dfrac{1}{3}[/tex] lies between 0 and 1. Therefore, the decay factor of the given exponential function is [tex]\dfrac{1}{3}[/tex].
Hence, the correct option is A.
Answer:
Step-by-step explanation:
2
Which is the length of the building's wall brace?
A. 14.45 m
B. 17 m
C. 23 m
D. 49 m
E. 189 m
Answer:
A) 14.45 m is the answerrrerreer
Answer:
17m
Step-by-step explanation:
We can use the Pythagorean theorem
a^2+b^2= c^2 where a and b are the legs and c is the hypotenuse
8^2 + 15^2 = c^2
64+ 225 = c^2
289 = c^2
Taking the square root of each side
sqrt(289) = sqrt(c^2)
17 =c
Jeremy is training for a race. When he
trains, he runs on a path that is
1.25 miles long. Last week, Jeremy ran
on the path 7 times. How many miles
did Jeremy run on the path last week?
What is an equation of the line that passes through the point (2;8) and has a slope of 3?A.y= 3x-2
B.y= 3x-22
C.y= 3x+ 2
D.y= 3x+ 22
Answer:
The letter C is the answer.
2. Write an inequality for each of the
following situations:
The temperature was less than 7° F.
You must be at least 42 inches tall to ride
the rollercoaster.
The repairs to the car will be at least $125.
You need to sell atleast 25 tickets.
You cant be more than 40 pounds to ride the ponies
There were less than 12 people in my class
Answer:
the temperature is 6 degress fair hight you are 42inches while riding the ride
Given JKMN is a square and NM= 4x and KM = 6x - 16, find all missing angle measures and side lengths.
Answer:
The side lengths are 32 units each
Step-by-step explanation:
Given
[tex]NM= 4x[/tex]
[tex]KM = 6x - 16[/tex]
Required
The side lengths and missing angles
Since JKMN is as square, then:
[tex]NM = KM[/tex] -- all sides are equal
[tex]4x = 6x - 16[/tex]
Collect like terms
[tex]4x - 6x = - 16[/tex]
[tex]-2 x = - 16[/tex]
Divide by -2
[tex]x = 8[/tex]
Substitute [tex]x = 8[/tex] in [tex]NM= 4x[/tex]
[tex]NM = 4 * 8[/tex]
[tex]NM = 32[/tex]
The missing angles can't be solved without an attachment.
However, if the missing angles are the angles at the edges of the square, then they measure 90 degrees each (i.e. angles at right angle)
Find the y-intercept and the x-intercept of the line below.
Answer:
the x- intercept is 1
the y-intercept is 2
3 (4y + 1 ) -20 help
Answer:
-5
Step-by-step explanation:
3x4=12
3x1=3
12y+3
15-20=
-5
【☆】★【☆】★【☆】★【☆】★【☆】【☆】★【☆】★【☆】★【☆】
My approach to this problem was to simplify the expression.
3( 4y + 1) - 20y
12y + 3 - 20y (expanded the brackets)
-8y + 3 (collected like terms)
The answer is B.
【☆】★【☆】★【☆】★【☆】★【☆】【☆】★【☆】★【☆】★【☆】
8x+20y=-120 as slope
Answer:
y = -2/5x -6
slope is -2/5
y intercept -6
Step-by-step explanation:
8x+20y=-120
Slope intercept form is y = mx+b where m is the slope and b is the y intercept
Subtract 8x from each side
8x -8x+20y= -8x-120
20y = -8x - 120
Divide by 20
20y/20 = -8x/20 -120/20
y = -2/5x -6
9. What property was used to get from line 1 to line 2?
line 1: 16 + 3x + 5 + 2x
line 2:2x + 3x + 5 + 16
line 3:5x + 21
Answer: Commutative Property of Addition
This property says that A+B = B+A. The order of addition doesn't matter.
As an example, 2+3 = 3+2 since both sides evaluate to 5.
I could use some help on this, thank you!
Answer:
B
Step-by-step explanation:
[tex]y = 3x - 5 = 37 \\ 3 \times 14 = 42 \\ 42 - 5 = 37[/tex]
PLSSS HELP!! (Determine the value of x.)
Answer:
X=4
Step-by-step explanation:
(2x-5)+(4x-1)=7x-10
2x-5+4x-1=7x-10
6x-6=7x-10
6x=7x-4
x=4
You invest $10,200 in an account that compounds continuously at an annual percent interest rate of 6.25%. How long does it take to double your money?
Answer:
11.09 years
Step-by-step explanation:
Given data
Principal P= $10200
Rate= 6.25%
Double the principal A = $20,400
The expression for the time taken is
t= ln(A/P)/r
t= ln(20400/10200)/0.0625
t= ln(2)/0.0625
t= 0.69314/0.0625
t= 11.09024 years
Hence the number of years is 11.09 years
The population of fish in a pond is given by the function P(t), where t is the number of months after June. Interpret the statements P(0) = 1,023 and P(2) = 1,612.
A. The population of fish in the pond was reduced by 589 fish and the population of fish in August was 1,612.
B. The population of fish in the pond was reduced by 589 fish and the population of fish in September was 1,612.
C. The population of fish in the pond grew by 589 fish and the population of fish in August was 1,612.
D. The population of fish in the pond grew by 589 fish and the population of fish in September was 1,612.
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the image in down there attached
Answer:
D
Step-by-step explanation:
For this one, you want to solve it similarly to linear equations.
-13x+11<-24x by adding 24x to both sides becomes 11x<11.
From there, you divide by 11 to isolate x, leaving x<1.
Since the equation has a < symbol (not ≤), the dot is not filled in. X is less than 1, so the arrow goes to the left, making it D.
**This content involves solving and sketching linear inequalities, which you may wish to revise. I'm always happy to help!
What is the equation of the line that is parallel to the line x = -2 and passes through the point (5.4)?
Lines parallel to each others only occur when two slopes of equations are same. The definition of parallel lines is:
[tex] \large \boxed{m_1 = m_2}[/tex]
We are given the equation of a line which is x = -2. For x = a, the equation forms a verical line and has an undefined slope. These below are basic that you may need to learn when learning about the line graph:
y = a —> horizontal line; slope is 0.x = a —> vertical line; slope is undefined.For y = a, any a-values would have same x-values. For example, if we are given y = 2 then any domains or x-values can have the range of 2.For x = a, any a-values would have same y-values or range.Back to the question. We want to find the equation of a line that is parallel to the line x = -2 and passes through (5,4) point. Recall the definition of parallel line that both slopes of equations must equal. Since x = a for any a-values would give an undefined slope. That means our parallel would be x = b.
Because the line passes through (5,4) - for any a-values from x = a would give out the set of all real numbers for range. Therefore the equation of a line is x = 5.
Answer
The equation of a line that is parallel to x = -2 and passes through (5,4) is x = 5.I hope this helps! If you have any doubts or questions, don't hestitate to ask in comment! Good luck on your assignment and have a great day!
Please help I’ll give brainliest
Please help me
I just need to find the measure of every angle
Answer: 108 use a ruler
Step-by-step explanation:
The following table represents the highest educational attainment of all adult
residents in a certain town. If a resident who is aged 40-49 is chosen at random, what
is the probability that they have completed a master's degree? Round your answer to
the nearest thousandth.
Answer:
≈0.576
Step-by-step explanation:
Age under 40: 871+870=1741
Total with master’s degree: 3023
Probability: 1741/3023
≈0.576
Seven pounds of nuts are shared equally among 5 scouts how much does each scoct get
help please this should be turn in 5mijs please
Math help due soon thanks
Which variable in the following equation represents the slope of the line? y=mx+b
Simplify. Remove all perfect squares from inside the square root.
[tex] \sqrt{30b { }^{5} } [/tex]
5x + 14 = −7
solve help me
Answer:
x = -4 1/5
Step-by-step explanation:
5x + 14 = -7
5x = -21
-21/5 = -4 1/5
Hope this is correct. Have a great day.
Answer:
[tex] \frac{ - 21}{5} \: or \: - 4 \frac{1}{5} \: or \: - 4.2[/tex]
Step-by-step explanation:
[tex]5x+14=−7 \\ 5x=−7−14 \\ 5x=−21 \\ x = \frac{ - 21}{5} \\ x = - 4.2[/tex]
In Mixed fraction.
[tex]x = - 4 \frac{1}{5} [/tex]
Hope it is helpful....Me need help on this
Answer:
1385 mi to find the area A=21(21)(3.14)
A=441(3.14)
1384.74 round to the nearest 10th is 1385
Rebecca is comparing two prices of peanut
butter. Peanut butter A has 12 ounces and
costs $6.00. Peanut butter B has 32 ounces and
costs $18.00. Which one is a better buy?
Answer:
Peanut butter A is the better buy,
Step-by-step explanation:
To compare them directly, we can find the price per ounce for each peanut butter.
Peanut butter A has 12 ounces and costs $6, thus, each ounce is [tex]\frac{6}{12}=\$0.50[/tex]
Peanut butter B has 32 ounces and costs $18, thus, each once is [tex]\frac{18}{32}\approx\$0.56[/tex]
Therefore, Peanut butter A is the better buy.
Let U(-7,5) and V(4, -3). What is the length of UV? Round your answer to the nearest 10th
Answer:
13.60units
Step-by-step explanation:
Given data
U(-7,5) and V(4, -3)
x1=-7
y1=5
x2= 4
y2= -3
The expression for the distance between two points is
d=√((x_2-x_1)²+(y_2-y_1)²)
substitute
d=√((4-(-7))²+(-3-5)²)
d=√((4+7))²+(-8)²)
d=√(11)²+(-8)²)
d=√121+64
d=√185
d=13.60units
Hence the distance is 13.60units